Let x₁ and x₂ be the real roots of the equation $${x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0$$, then maximum value of $$x_1^2 + x_2^2$$ is

When x¹⁰⁰ is divided by x² $$-$$ 3x + 2, the remainder is (2^{k + 1} $$-$$ 1)x $$-$$(2^k $$-$$ 1), then k is